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Appendix VL

and adopting the method of p. 852. The scale/ measures the
accelerative value, and the correlation of all the scales will be
understood from p. 853.

Pp. 478 and 680.   Energy of Rotation.—At the former
of these pages the energy of a rotating body was shewn to be

•0001714 mR2N2 foot pounds .................. (i)

where R = average radius of rotation in feet, or radius of gyra-
tion. Now * revolutions per minute' is only a practical way of
stating angular velocity:

.*. Energy of rotation = — = -         foot pounds.

Taking I as moment of inertia of the body in inch Ib. units, and
m a small element ot mass acting at a radius r^ inches, we have

1=  S mr?   =   ~ R2-122 in gravity units


or   =   w R2-i22 in absolute units.

The second is the usual method of expressing I, and will be
here adopted    Then—
Energy of rotation = ?!_J1   =   —JlL-. footpounds ... (2)

And from (i) this also

•0001714 -~.N2foot pounds (3)


Note carefully that while I is generally measured in inches
and Ibs. it must be changed to feet and Ibs. when inserting in the
energy formula, or wfi becomes w R2 x i22, and ze/R2 = I -~ i22.
We see then there are two methods of expressing the energy, one
in N and one in w.

Graphically.—The value of r2 (radius of gyration squared)
being known, that of I can be obtained. The graphic solution
Ifor r® for any solid of revolution is explained at pp. 681 and 845 ;
but for certain regular solids, such as cylinders and rings, we may
froceed by a method similar to that on p. ^419. In Fig. 970 is
shewn a cylinder of radius r0 whose I is required round the